The cosparse analysis model as the corresponding version of the sparse synthesis model has drawn much attention in recent years. Many approaches have been proposed to solve this model. In some conventional general, these methods usually relaxedl0-norm tol1-norm orl2-norm to represent the cospas...
We consider the class of subgradient methods for solving minimization of a nonsmooth convex function regularized by the discretized $$\\ell _1$$1 norm models arising in image processing. This class ofdoi:10.1007/s11760-015-0815-zAbdelkrim El Mouatasim...
Our approach uses the l1-norm as a regularization on the inverse covariance matrix. We utilize a novel projected gradient method, which is faster than previous methods in practice and equal to the best performing of these in asymptotic complexity. We also extend the l1-regularized objective to ...
trainingL1-normandL2-normSVMclassifier.Introduction1Subgradientmethods:generalizationofthegradientmethodsfornon-differentiableconvexfunctions.Motivation:Simpleandgeneralmethodforconvexproblems.Forexample,usefulforlarge-scaleLinearProgramming,QuadraticProgrammingandSemidefiniteProgrammingproblems.Outline: Subgradientand...
图1:在x1处,凸函数f是可微的,并且g1(即函数f在x1处的偏导数)是在x1处的唯一次梯度。在点x2处,函数不可微,并且在该点处,函数f有很多次梯度:图中演示了g2,g3两个次梯度。 图2:当且仅当(g,-1)定义了上镜图f在(x,f(x))处的一个支撑超平面,那么矢量g∈Rn是函数f在x处的一个次梯度。